I am working on below statement:
A is an $m \times n$ matrix, and $\lambda$ is an eigenvalue of $(A^T)A$ which eigenvector $X$ doesn't equal to zero. Show that $\lambda$ is greater than or equal to zero.
I started from computing $||AX||^2$, then ended up with $\lambda\cdot (X^T)\cdot X$ is greater than or equal to zero. Then how can I know $(X^T)\cdot X$ is greater than zero?